A293407 Least integer k such that k/n^2 > (-1 + sqrt(5))/2 (the golden ratio).

0, 1, 3, 6, 10, 16, 23, 31, 40, 51, 62, 75, 89, 105, 122, 140, 159, 179, 201, 224, 248, 273, 300, 327, 356, 387, 418, 451, 485, 520, 557, 594, 633, 674, 715, 758, 801, 847, 893, 941, 989, 1039, 1091, 1143, 1197, 1252, 1308, 1366, 1424, 1484, 1546, 1608, 1672

Offset

0,3

Links

Clark Kimberling, Table of n, a(n) for n = 0..1000

Formula

a(n) = ceiling(r*n^2), where r = (-1 + sqrt(5))/2.

a(n) = A152738(n) + 1 for n > 0.

Mathematica

z = 120; r = -1+GoldenRatio;
Table[Floor[r*n^2], {n, 0, z}];   (* A152738 *)
Table[Ceiling[r*n^2], {n, 0, z}]; (* A293407 *)
Table[Round[r*n^2], {n, 0, z}];   (* A293408 *)

Crossrefs

Cf. A001622, A293401, A293403, A152738, A293408.

Sequence in context: A294481 A049697 A111712 * A194144 A330133 A025701

Adjacent sequences: A293404 A293405 A293406 * A293408 A293409 A293410

Keyword

nonn,easy

Author

Clark Kimberling, Oct 11 2017

Status

approved